Power spectrum of the primordial scalar field fluctuations in the warm inflation scenario

Abstract

A new model of warm inflation without slow-roll conditions for the scalar field is studied. Classicality conditions that must be satisfied to have an effective stochastic approach in the warm inflation scenario are analyzed for a general coarse-grained field, defined with a function that describes the long wavelength suppression. The theory can predict the spectral density of the fluctuations of the field which can be compared with the COBE data. @S0556-2821~98!11020-2# PACS number~s!: 98.80.Cq, 05.40.1j, 98.70.Vc In 1995 Berera and Fang @1# showed how thermal fluctuations during inflation may play the dominant role in producing the initial perturbations, invoking the slow-roll approximation through a combination of a flat potential and dissipative damping. This idea was extended in @2,3# into the warm inflation scenario. This scenario differs from supercooled inflation scenarios in that reheating is no longer necessary and de Sitter expansion and radiation energy production occur together. The Universe we will consider is still dominated by the vacuum energy of the field, with the thermal component being small. The motivation of this work is the study of the quantum to classical transition in the warm inflation scenario and the spectral density of the fluctuations of an arbitrary coarsegrained scalar field. In this work I consider a general case, where the dynamics of a scalar field is minimally coupled to a classical gravitational one. The system is described by the Lagrangian